adaptive robust control f or dual stage hard drives
DESCRIPTION
in GOD we trust. Adaptive Robust Control F or Dual Stage Hard Drives. استاد راهنما : جناب آقای دکتر حمید تقی راد. Dr. Hamid D. Taghirad. هادی حاجی اقراری دانشجوی کارشناسی ارشد مهندسی برق – کنترل دانشگاه خواجه نصیرالدین طوسی. H.H.Eghrary MS Student of Electrical Engineering - PowerPoint PPT PresentationTRANSCRIPT
Adaptive Robust Adaptive Robust ControlControl F Foror Dual Stage Dual Stage
Hard DrivesHard Drives
راهنما : راهنما :استاد حمید استاد دکتر آقای حمید جناب دکتر آقای جنابراد راد تقی تقیاقراری حاجی هادی
برق مهندسی ارشد کارشناسی کنترل–دانشجویطوسی نصیرالدین خواجه دانشگاه
Dr. Hamid D. Taghirad
H.H.EghraryMS Student of Electrical EngineeringK.N.Toosi Univ.
2end Seminar Presentation 2end Seminar Presentation
Introduction to Adaptive Robust ControlIntroduction to Adaptive Robust Control
• Obstacles for Control Algorithm DesignObstacles for Control Algorithm Design
• Strategies for Performance Strategies for Performance ImprovementImprovement• Adaptive Robust Control (ARC) Adaptive Robust Control (ARC) For a For a HDDHDD Adaptive Control
Robust Control
• ARC via Discontinuous ProjectionARC via Discontinuous Projection
• ARC via Smooth ProjectionARC via Smooth Projection
• Desired Compensation Desired Compensation ARCARC
Sunday, August 12,2007
Obstacles for Control Algorithm Obstacles for Control Algorithm Design:Design:
•Inherent Nonlinearity
•Modeling Uncertainty
• Unknown But Reproducible
• for example: Unknown parameters
• Unreproducable
for example: model Disturbance
Strategies for Performance Strategies for Performance Improvement:Improvement:
•Nonlinear Analysis And SynthesisNonlinear Analysis And Synthesis
Deal With Nonlinearity Directly : Nonlinear Nonlinear ControlControl
•Fast Robust FeedbackFast Robust Feedback
Effective for both reproducible and none Reproducible Uncertainities
•Controled Learning For Uncertainity ReductionControled Learning For Uncertainity Reduction
Effective for Reproducible Uncertainities
Adaptive Robust ControlAdaptive Robust Control (ARC)(ARC)RobusRobustt
AdaptiveAdaptive
Drawbacks:•Transient Performance of the system is not Clear.•Unknown Nonlinear functions such as external disturbances are not considered.
Drawbacks:•Transient Performance of the system is not Clear.•Unknown Nonlinear functions such as external disturbances are not considered.
•Reduce the model uncertainty
•Zero Tracking Error (Without High gain Feedback)
•Attenuate the effect of model uncertainties throughrobust feedback.•InstantaneousReaction
Deterministic Robust ControlDeterministic Robust Control
•Use to Design Base Line Controller
Guarantee Guarantee Transient PerformanceTransient Performance Prescribed final tracking accuracyPrescribed final tracking accuracy
Adaptive ControlAdaptive Control
•Used to Design Supervisor
Improved Improved Asymptotic Input TrackingAsymptotic Input Tracking
Conventional Adaptation Law Estimated Parameters May not be Bounded
Deterministic Robust Control Requires Bounds On Uncertainties
Modify The Conventional Adaptation Law
Bounded Estimation ParametersBounded Estimation Parameters
Adaptive Robust ControlAdaptive Robust Control ForFor Hard Disk Drive Servo Hard Disk Drive Servo SystemSystem
x =x1 2
jx =u-Bx -A sign(x )-F +Fhys d2 2 f 2
y =x1
Tf fj B A d
d hys nd F F d d
min max:
:d dd d d
. . .1 2 3 4 d
x = x1 2
x =u- x - sign(x )-2 2 2
y =x1
Adaptive Control scheme: Robust Control scheme:
Adaptive Control scheme:
Stability Analysis:
Lyapanov Function:
1 12 22 2
V ea
ˆ : Parameter Estimation
ˆ Estimation Error
2
1
1
( )
1
1 ˆ ˆ
ˆ
ˆ ˆ 0
T
T
T
ke
e
diag
e e
V ee ea
ke
2aV ke
ResultsResults:: 0
0T
et
•Limitations Of Adaptive ControlLimitations Of Adaptive Control
•Transient Performance is Unknown
•Uncertain nonlinearity are not Considered
0
Robust Control scheme:
More In Detail:More In Detail:
• Error Dynamics
20
~s
T Ukee
2sU Choose The such that:
0.
)~
.(
2
2
s
Ts
Ue
Ue
Stability Analysis:
Lyapanov Function:
2
2
1eVs
eeVs .
keUe sT
20
~
20 )
~(
2keUeV s
Ts
)~
(20 s
T Ue
2keVsChoose small such that:Choose small such that:
0sV : Stable: Stable
•Tracking Error
•Steady State Steady State ErrorError
ke
2
)(
Decrease for decreasing Steady State ErrorDecrease for decreasing Steady State Errork
e
2)(
Parameter AdaptationParameter Adaptation
)~
.(2
TsUe
Adaptive Robust ControlAdaptive Robust Control
Conventional Adaptation Law Estimated Parameters May not be Bounded
Deterministic Robust Control Requires Bounds On Uncertainties
Modify The Conventional Adaptation Law
Bounded Estimation ParametersBounded Estimation Parameters
Adaptive Robust ControlAdaptive Robust Control
Via Discontinuous ProjectionVia Discontinuous Projection
max minˆ
ˆ ˆ0, ( , 0) ( , 0)Pr ( )
,
e or eoj e
e otherwise
ˆPr ( )oj e
minˆ ˆ ˆ4. 0, 0
maxˆ ˆ ˆ1. 0, 0
minˆ ˆ ˆ2. 0, 0
maxˆ ˆ ˆ3. 0, 0
Remains in
Remains in
Decreases
Increases
min
max min maxˆ
Parameter Uncertainty Parameter Uncertainty Bounded Bounded via Adaptation Progressvia Adaptation Progress
RobustRobust ControlControl Problem SolvedProblem Solved
0
1( ) ( ( , ) )
0
V v dv
Adaptive Robust ControlAdaptive Robust Control
Via Smooth ProjectionVia Smooth Projection
There is a Lyapanov Function :There is a Lyapanov Function :
Stability is GuaranteedStability is Guaranteed
Desired Compensation Desired Compensation ARCARC Remind ARC SchemeRemind ARC Scheme
Real Parameter MeasurementReal Parameter Measurement(Measurement Noise)
Static FeedbackStatic Feedback
Desired TrajectoryDesired Trajectory
DynamicDynamicStabilizingStabilizingFeedbackFeedback
Desired Compensation Desired Compensation ARCARC
Regressors Dose not Depend On Measurements Regressors Dose not Depend On Measurements
Eliminate Measurement Noise Effect on Parameter AdaptationEliminate Measurement Noise Effect on Parameter Adaptation Off-Line Regressors CalculationOff-Line Regressors Calculation
Fast Error Dynamic and Parameter AdaptationFast Error Dynamic and Parameter Adaptation
Facilitate Control Gain Tuning Process due to Facilitate Control Gain Tuning Process due to Separation of Robust Control And Parameter AdaptationSeparation of Robust Control And Parameter Adaptation